Homework Help:
Determining Time When Comparing Two Equations

The last time I used these forums for help I got awesome responses. And here I am again needing help. Thought I'd just mosey on over and pop up my question I got. Here it is:

(2) A car and motorcycle start from rest at the same time form rest on a straight track, but the motorcycle is 25.0 m behind the car. The car accelerates at a uniform rate of 3.70 m/s2 and the motorcycle accelerates at a uniform rate of 4.40 m/s2.
(a) How much time elapses before the motorcycle overtakes the car?

I know that I need this formula --> d = Vi(t) + 1/2(a)(t^2)
And I know that it should be set up so that the two distance equations (one for the car and one for the motorcycle) are set equal to each other, so I can further solve the junctioned equation for (t). But, I seem to be having some trouble. I need to know how to go about solving this problem. Any help is very much appreciated! Thanks a lot.

The formula "d = Vi(t) + 1/2(a)(t2)" isn't quite correct. It should be d = Vi(t) + 1/2(a)(t2)+ di where di is the initial distance from some reference point.

In this case, if you take the point from which the motorcycle starts as the reference point, then di= 0 for the motorcycle and di= 25 for the car (since the car starts 25 meters ahead of the motorcycle).
Of course, Vi= 0 for both motorcycle and car.

... excuse my lack of knowledge in this area but next am I supposed to square each side of the equation or divide the right side by (1.85)? Or is it something completely different. I seriously must be having an off day... *embarassment* This usually doesn't happen... I've tried a few things on it but I have no idea what the right answer is... that's my problem right now...